帽子游戏建设者的力量
The Hats game. The power of constructors
摘要：
我们分析以下确定性帽子博弈的一般版本。几个戴着彩色帽子的圣人占据了一个图的顶点。每个圣人可以有一顶$k$颜色的帽子。每个圣人都试图猜测自己的帽子的颜色，只是根据观察他的邻居的帽子，而不交换任何信息。如果一个预先确定的猜测策略保证每个颜色分配至少有一个正确的个人猜测，那么它就是获胜的。我们提出了一个可平面图的例子，其中的圣人赢得了$k = 14$。我们也给出了一个简单的证明定理的帽子游戏的“风车”图。
英文摘要：
We analyze the following general version of the deterministic Hats game. Several sages wearing colored hats occupy the vertices of a graph. Each sage can have a hat of one of $k$ colors. Each sage tries to guess the color of his own hat merely on the basis of observing the hats of his neighbors without exchanging any information. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colors. We present an example of a planar graph for which the sages win for $k = 14$. We also give an easy proof of the theorem about the Hats game on "windmill" graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
